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Is xy > (x^2)(y^2)?

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NandishSS Master | Next Rank: 500 Posts Default Avatar
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Is xy > (x^2)(y^2)?

Post Sun Jan 15, 2017 5:13 am
Is xy > (x^2)(y^2)?
(1) 4x^2 = 19
(2) y^2 = 1

OA:C

Source:Math Revolution

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Post Sun Jan 15, 2017 10:13 pm
NandishSS wrote:
Is xy > (x^2)(y^2)?
(1) 4x^2 = 19
(2) y^2 = 1

OA:C

Source:Math Revolution
We have a situation: Is xy > (xy)^2?

Whether one/both of x and y is/are positive/negative, RHS [(xy)^2] is positive. So we must focus our energy on whether xy is positive and is greater than (xy)^2 or not.

S1:
4x^2 = 19 => x =(19/4)^(1/2) => x can be positive/negative
We do not have any information about y. S1 itself is insufficient.

S2:
y^2 = 1 => y = +/-1.
We do not have any iformation about x. S2 itself is insufficient.

S1 and S2:
By plugging in the value of x and y, we get,

[+/-(19/4)^(1/2)]*[+/-1] > [19/4]*[1]?

If we take the product of x and y positive, then

|(19/4)^(1/2)| > 19/4?, the answer is NO. The square root of a number greater than 1 (19/4 > 1) is less than the number.

If we take the product of x and y negative, then

-|(19/4)^(1/2)| > 19/4?, the answer is NO. LHS is negative and RHS is positive.

Sufficient.

Answer: C

-Jay
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Post Sun Jan 15, 2017 5:34 pm

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Post Sun Jan 15, 2017 10:13 pm
NandishSS wrote:
Is xy > (x^2)(y^2)?
(1) 4x^2 = 19
(2) y^2 = 1

OA:C

Source:Math Revolution
We have a situation: Is xy > (xy)^2?

Whether one/both of x and y is/are positive/negative, RHS [(xy)^2] is positive. So we must focus our energy on whether xy is positive and is greater than (xy)^2 or not.

S1:
4x^2 = 19 => x =(19/4)^(1/2) => x can be positive/negative
We do not have any information about y. S1 itself is insufficient.

S2:
y^2 = 1 => y = +/-1.
We do not have any iformation about x. S2 itself is insufficient.

S1 and S2:
By plugging in the value of x and y, we get,

[+/-(19/4)^(1/2)]*[+/-1] > [19/4]*[1]?

If we take the product of x and y positive, then

|(19/4)^(1/2)| > 19/4?, the answer is NO. The square root of a number greater than 1 (19/4 > 1) is less than the number.

If we take the product of x and y negative, then

-|(19/4)^(1/2)| > 19/4?, the answer is NO. LHS is negative and RHS is positive.

Sufficient.

Answer: C

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Hyderabad | Mexico City | Toronto | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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